1. Technical Field
The present invention relates to modulation and demodulation of information and more particularly to a two-stage low-complexity table-driven Max-Log bit-by-bit log-likelihood ratio (LLR) calculator and method.
2. Description of the Related Art
In many modern communication systems, where a soft decoder is employed, it is necessary to calculate a soft estimate for data bits from received signals. A maximum a posteriori (MAP) demodulator can be used to generate the bit-by-bit log-likelihood ratio (LLR), this is too complex for the practical implementation.
To avoid the ultra-high complexity of the MAP algorithm, Max-Log is practically used to compute the LLR, e.g., it is included in the 3GPP standard (Section A.1.4 of 3GPP TS 25.848). However, the complexity of Max-Log is high even for a constellation of moderate size, say, 64-QAM (Quadrature Amplitude Modulation) if no further simplification is considered.
For QAM constellations, based on the observation that a properly designed QAM constellation can be decomposed into two PAM (Pulse Amplitude Modulation) constellations, (see e.g., X. Gu, K. Niu, and W. Wu, “A novel efficient soft output demodulation algorithm for high order modulation,” in Proc. 4th Int. Conf. Computer Inform. Technol., Wuhan, China, September 2004, pp. 493-498 (hereinafter Gu et al.). This greatly reduces the complexity.
For PSK constellations, K. Fagervik and T. G. Jeans, in “flow complexity bit by bit soft output demodulator,” Electron. Lett., vol. 32, pp. 985-987, May 1999 (hereinafter Fagervik et al.), proposed an approximate Max-Log, which is less complex compared to the exact Max-Log with negligible performance loss. However, the complexity of the above state-of-the-art demodulators is still very high if high-order modulations are used, say, 1024-QAM and 32-PSK. The algorithms in Gu et al. and Fagervik et al. require many operations such as multiplications, additions, and comparisons to obtain results.